The reduced transition matrix in chaotic dual-unitary quantum circuits has low-rank structure with entropy growing at most logarithmically in time, enabling efficient approximation for local expectation values.
Mirsky, Symmetric gauge functions and unitarily in- variant norms, The quarterly journal of mathematics11, 50 (1960)
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Low Rank Structure of the Reduced Transition Matrix
The reduced transition matrix in chaotic dual-unitary quantum circuits has low-rank structure with entropy growing at most logarithmically in time, enabling efficient approximation for local expectation values.